# Single Acting vs Double Acting Pneumatic Cylinder: Which Design Delivers Better Performance for Your Application?

> Source: https://rodlesspneumatic.com/blog/single-acting-vs-double-acting-pneumatic-cylinder-which-design-delivers-better-performance-for-your-application/
> Published: 2025-07-13T03:54:07+00:00
> Modified: 2026-05-09T04:06:10+00:00
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## Summary

Single acting vs double acting pneumatic cylinders differ in air-port design, return method, force control, and automation suitability. This guide compares construction, operating characteristics, applications, cost trade-offs, and selection factors for engineers specifying pneumatic cylinder systems.

## Article

![MY1B Series Type Basic Mechanical Joint Rodless Cylinders](https://rodlesspneumatic.com/wp-content/uploads/2025/05/MY1B-Series-Type-Basic-Mechanical-Joint-Rodless-Cylinders-1.jpg)

[MY1B Series Type Basic Mechanical Joint Rodless Cylinders](https://rodlesspneumatic.com/products/pneumatic-cylinders/my1b-series-type-basic-mechanical-joint-rodless-cylinders-compact-versatile-linear-motion/)

Engineers frequently select the wrong pneumatic cylinder type for their applications, leading to inadequate performance, excessive energy consumption, and costly system modifications that could have been avoided with proper initial selection.

**[Single-acting pneumatic cylinders use compressed air for movement in one direction only with spring or gravity return](https://eng.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/Fluids_1%3A_Fluid_Power_and_Pneumatics_%28NWTC%29/06%3A_Single-Acting_Cylinders/6.02%3A_Single-Acting_Cylinder_Operation)[1](#fn-1), while double-acting cylinders use air pressure for both extension and retraction, providing superior force control, positioning accuracy, and operational flexibility for most industrial applications.**

Last month, Sarah from a Wisconsin food processing plant contacted me after her single-acting cylinders couldn’t provide adequate retraction force for her packaging line, resulting in $35,000 in lost production before switching to our double-acting [rodless cylinders](https://rodlesspneumatic.com/blog/what-is-a-rodless-cylinder-and-how-does-it-transform-industrial-automation/) restored full operational control.

## Table of Contents

- [What Are the Fundamental Design Differences Between Single and Double Acting Cylinders?](#what-are-the-fundamental-design-differences-between-single-and-double-acting-cylinders)
- [How Do Operating Characteristics Compare Between These Cylinder Types?](#how-do-operating-characteristics-compare-between-these-cylinder-types)
- [Which Applications Benefit Most from Single Acting vs Double Acting Designs?](#which-applications-benefit-most-from-single-acting-vs-double-acting-designs)
- [What Are the Cost and Performance Trade-offs Between These Cylinder Types?](#what-are-the-cost-and-performance-trade-offs-between-these-cylinder-types)

## What Are the Fundamental Design Differences Between Single and Double Acting Cylinders?

Understanding the core design differences between single-acting and double-acting pneumatic cylinders is essential for making informed selection decisions that optimize system performance and cost-effectiveness.

**Single-acting cylinders feature one air port and use compressed air for powered movement in one direction with spring return, while [double-acting cylinders have two air ports enabling powered movement in both directions](https://eng.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/Fluids_1%3A_Fluid_Power_and_Pneumatics_%28NWTC%29/04%3A_Basic_Circuits_using_Cylinders/4.01%3A_Actuators_-_Cylinders)[2](#fn-2) through alternating air supply to opposite sides of the piston.**

![A technical illustration comparing a single-acting cylinder, which uses one air port and a spring for its return stroke, with a double-acting cylinder, which uses two air ports for powered movement in both extend and retract directions.](https://rodlesspneumatic.com/wp-content/uploads/2025/07/Single-Acting-vs.-Double-Acting-Cylinder-1024x881.jpg)

Single-Acting vs. Double-Acting Cylinder

### Single-Acting Cylinder Construction

#### Core Components

Single-acting cylinders contain these essential elements:

- **Single air port**: Located at one end for air supply
- **Return spring**: Provides force for return movement
- **Piston assembly**: Sealed piston with one-way air chamber
- **Exhaust port**: Allows air escape during spring return
- **Spring chamber**: Houses return spring mechanism

#### Spring Return Mechanism

The return spring serves multiple functions:

- **Return force**: Provides energy for retraction movement
- **Position holding**: Maintains extended or retracted position
- **Fail-safe operation**: Returns cylinder to safe position on air loss
- **Speed control**: Spring rate affects return speed

### Double-Acting Cylinder Construction

#### Dual Chamber Design

Double-acting cylinders feature:

- **Two air ports**: Port A and Port B for bidirectional air supply
- **Divided piston**: Separates cylinder into two independent air chambers
- **Sealed chambers**: Prevent air mixing between extension and retraction sides
- **Rod sealing**: Maintains pressure integrity with external rod

#### Control System Requirements

Double-acting operation requires:

| Component | Single-Acting | Double-Acting | Function |
| Directional valve | 3-way valve | 4-way or 5-way valve | Air flow control |
| Air connections | 1 supply line | 2 supply lines | Pressure delivery |
| Exhaust ports | 1 exhaust | 2 exhausts | Air discharge |
| Flow controls | 1 control | 2 controls | Speed regulation |

### Internal Pressure Dynamics

#### Single-Acting Pressure Profile

Single-acting cylinders experience:

- **Extension**: Full supply pressure on piston face
- **Retraction**: Atmospheric pressure with spring force only
- **Holding**: Supply pressure maintains position against spring
- **Air consumption**: Only during extension movement

#### Double-Acting Pressure Profile

Double-acting cylinders provide:

- **Extension**: Supply pressure to cap end, exhaust from rod end
- **Retraction**: Supply pressure to rod end, exhaust from cap end
- **Position holding**: Maintained pressure in active chamber
- **Force modulation**: Variable pressure for different force requirements

At Bepto, we manufacture both single-acting and double-acting rodless cylinders, with our double-acting designs representing 85% of customer selections due to their superior control capabilities and operational flexibility.

## How Do Operating Characteristics Compare Between These Cylinder Types?

The operational differences between single-acting and double-acting pneumatic cylinders significantly impact their suitability for various industrial applications and performance requirements.

**Double-acting cylinders provide 3-5 times greater retraction force, 50-80% better positioning accuracy, variable speed control in both directions, and superior load handling capability compared to single-acting cylinders that rely on spring return with limited force and control.**

![An infographic comparing the performance of double-acting and single-acting cylinders. The double-acting side lists its advantages in force, accuracy, speed control, and load handling, while the single-acting side highlights its limitations.](https://rodlesspneumatic.com/wp-content/uploads/2025/07/Double-Acting-vs.-Single-Acting-Cylinder-Performance-1024x1024.jpg)

Double-Acting vs. Single-Acting Cylinder Performance

### Force Output Comparison

#### Extension Force Capabilities

Both cylinder types can provide full rated force during extension:

- **Single-acting**: Force = Pressure × Piston Area
- **Double-acting**: Force = Pressure × Piston Area
- **Performance**: Equal extension force capability

#### Retraction Force Analysis

Retraction force reveals significant differences:

| Cylinder Type | Retraction Force Source | Typical Force Range | Load Capability |
| Single-acting | Return spring only | 10-25% of extension | Light loads only |
| Double-acting | Full air pressure | 60-80% of extension | Heavy loads capable |
| Spring-return | Spring + air assist | 30-50% of extension | Medium loads |

### Speed and Control Characteristics

#### Speed Control Capabilities

Speed control options vary dramatically:

**Single-Acting Speed Control:**

- **Extension**: Meter-in or meter-out flow control
- **Retraction**: Spring rate and exhaust restriction only
- **Consistency**: Variable speed based on load changes
- **Precision**: Limited control accuracy

**Double-Acting Speed Control:**

- **Extension**: Full flow control with meter-in/out options
- **Retraction**: Independent flow control system
- **Consistency**: Maintained speed regardless of load
- **Precision**: High accuracy positioning capability

#### Positioning Accuracy

Positioning performance differs significantly:

| Performance Factor | Single-Acting | Double-Acting | Improvement |
| Repeatability | ±2-5mm typical | ±0.1-0.5mm typical | 90% better |
| Load sensitivity | High variation | Minimal variation | 80% better |
| Temperature effects | Significant | Minimal | 70% better |
| Wear compensation | Poor | Excellent | 85% better |

### Energy Efficiency Analysis

#### Air Consumption Patterns

Energy usage varies between designs:

**Single-Acting Consumption:**

- **Extension**: Full air volume consumed
- **Retraction**: No air consumption (spring powered)
- **Holding**: Continuous air supply required
- **Overall**: Lower total air consumption

**Double-Acting Consumption:**

- **Extension**: Full air volume to cap end
- **Retraction**: Full air volume to rod end
- **Holding**: Pilot air only with proper valving
- **Overall**: Higher air consumption but better efficiency

### Cycle Rate and Productivity

#### Maximum Operating Speeds

Cycle rate capabilities show clear differences:

**Single-Acting Limitations:**

- **Extension speed**: Limited by air flow capacity
- **Retraction speed**: Fixed by spring characteristics
- **Cycle rate**: Typically 20-60 cycles per minute
- **Productivity**: Constrained by return speed

**Double-Acting Advantages:**

- **Extension speed**: Optimized through flow control
- **Retraction speed**: Independently controlled
- **Cycle rate**: Up to 300+ cycles per minute possible
- **Productivity**: Maximized through speed optimization

### Environmental Adaptability

#### Temperature Effects

Operating temperature impacts differ:

- **Single-acting**: Spring rate changes affect performance
- **Double-acting**: Minimal temperature sensitivity
- **Cold weather**: Springs become stiffer, affecting return
- **Hot conditions**: Spring relaxation reduces return force

#### Mounting Orientation Sensitivity

Gravity effects vary by design:

- **Single-acting**: Performance varies with mounting angle
- **Double-acting**: Consistent performance in any orientation
- **Vertical mounting**: Critical consideration for single-acting
- **Inverted operation**: May require spring assistance

Michael, a maintenance supervisor at a Michigan automotive plant, explained how switching from single-acting to our double-acting rodless cylinders transformed his assembly line: “We went from 45 cycles per minute to 120 cycles per minute, and our positioning accuracy improved so much that we eliminated a secondary adjustment station, saving $42,000 annually in labor costs.”

## Which Applications Benefit Most from Single Acting vs Double Acting Designs?

Different industrial applications have specific requirements that make either single-acting or double-acting pneumatic cylinders the optimal choice for performance, cost, and reliability.

**Single-acting cylinders excel in simple lifting, clamping, and safety applications where spring return provides fail-safe operation, while double-acting cylinders are essential for precision positioning, material handling, and high-speed automation requiring bidirectional force and control.**

### Ideal Single-Acting Applications

#### Safety and Fail-Safe Systems

Single-acting cylinders provide inherent safety advantages:

- **Emergency stops**: Spring return ensures [fail-safe operation on air loss](https://www.iacsengineering.com/fail-safe-system-design/)[3](#fn-3)
- **Safety guards**: Automatic retraction when air pressure drops
- **Brake systems**: Spring-applied, air-released brake mechanisms
- **Valve actuators**: Fail-safe positioning for process control

#### Simple Lifting and Clamping

Basic material handling benefits from single-acting design:

| Application Type | Why Single-Acting Works | Typical Force Range | Cycle Rate |
| Part ejection | Gravity assists return | 50-500 lbs | 30-80 CPM |
| Simple lifting | Load helps return | 100-2000 lbs | 20-60 CPM |
| Basic clamping | Spring provides release | 200-1500 lbs | 10-40 CPM |
| Gate operation | Weight assists closing | 300-3000 lbs | 5-30 CPM |

#### Cost-Sensitive Applications

Single-acting cylinders offer economic advantages:

- **Lower initial cost**: Simpler construction reduces price
- **Reduced air consumption**: Only extension uses compressed air
- **Simplified controls**: [3-way valve instead of 4-way valve](https://eng.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/Fluids_1%3A_Fluid_Power_and_Pneumatics_%28NWTC%29/07%3A_3_2_Directional_Control_Valves)[4](#fn-4)
- **Maintenance savings**: Fewer seals and moving parts

### Optimal Double-Acting Applications

#### Precision Manufacturing and Assembly

Double-acting cylinders excel in precision applications:

- **Component assembly**: Precise positioning and controlled force
- **Quality inspection**: Accurate probe positioning and movement
- **Material processing**: Controlled cutting, forming, and joining
- **Packaging operations**: Precise product handling and positioning

#### High-Speed Automation

Fast-cycle applications require double-acting performance:

**Packaging Line Applications:**

- **Product pushing**: Controlled acceleration and deceleration
- **Carton forming**: Precise folding and creasing operations
- **Label application**: Accurate positioning and pressure control
- **Quality rejection**: Fast, accurate product removal

#### Material Handling Systems

Complex material handling benefits from bidirectional control:

| Handling Task | Extension Function | Retraction Function | Performance Benefit |
| Pick and place | Extend to pick | Retract with load | Full force both ways |
| Conveyor transfer | Push product forward | Clear for next cycle | Precise timing |
| Sorting operations | Divert product | Return to position | High-speed operation |
| Loading systems | Position material | Return for next load | Consistent cycling |

### Specialized Application Considerations

#### Rodless Cylinder Applications

Rodless cylinders are typically double-acting because:

- **Long stroke capability**: Spring return impractical for long strokes
- **Precise positioning**: Accurate stops anywhere along stroke
- **Bidirectional loads**: Equal capability in both directions
- **Space efficiency**: Compact design requires powered return

#### Harsh Environment Applications

Environmental factors influence selection:

**Single-Acting Advantages:**

- **Contamination resistance**: Fewer seals and ports
- **Temperature stability**: Spring performance in extreme conditions
- **Simplicity**: Fewer failure points in harsh environments

**Double-Acting Advantages:**

- **Sealed operation**: Better contamination protection with proper sealing
- **Force consistency**: Unaffected by temperature variations
- **Reliability**: Predictable performance regardless of conditions

### Industry-Specific Preferences

#### Automotive Manufacturing

Automotive applications typically favor double-acting cylinders:

- **Assembly lines**: Precise part positioning and installation
- **Welding fixtures**: Controlled clamping and positioning
- **Material handling**: Accurate part transfer between stations
- **Quality control**: Precise inspection and testing operations

#### Food and Beverage Processing

Food processing applications vary by function:

- **Packaging**: Double-acting for precise control and speed
- **Safety systems**: Single-acting for fail-safe operation
- **Cleaning operations**: Double-acting for controlled movement
- **Product handling**: Application-specific selection based on requirements

#### Pharmaceutical Manufacturing

Pharmaceutical applications emphasize precision and cleanliness:

- **Tablet pressing**: Double-acting for precise force control
- **Packaging**: Double-acting for accurate positioning
- **Material handling**: Clean-room compatible double-acting designs
- **Quality control**: Precise positioning for inspection systems

At Bepto, we help customers select the optimal cylinder type for their specific applications. Our application engineers analyze force requirements, cycle rates, positioning accuracy, and environmental conditions to recommend the most cost-effective solution that meets performance requirements.

## What Are the Cost and Performance Trade-offs Between These Cylinder Types?

Understanding the total cost of ownership and performance implications helps engineers make informed decisions when selecting between single-acting and double-acting pneumatic cylinder designs.

**While single-acting cylinders cost 20-40% less initially and consume 30-50% less compressed air, double-acting cylinders provide 200-400% better productivity, 80-95% better positioning accuracy, and 40-60% lower maintenance costs, typically delivering positive ROI within 6-18 months in most applications.**

### Initial Investment Analysis

#### Purchase Price Comparison

Component costs vary significantly between designs:

| Cost Component | Single-Acting | Double-Acting | Price Difference |
| Cylinder body | $150-800 | $200-1200 | 25-50% higher |
| Control valve | $50-200 (3-way) | $80-350 (4-way) | 60-75% higher |
| Flow controls | $30-100 (1 unit) | $60-200 (2 units) | 100% higher |
| Installation | $100-300 | $150-450 | 50% higher |
| Total System | $330-1400 | $490-2200 | 30-60% higher |

#### System Complexity Factors

Double-acting systems require additional components:

- **Additional air lines**: Second supply line and fittings
- **More complex valving**: 4-way or 5-way directional control
- **Dual flow controls**: Independent speed control for each direction
- **Enhanced controls**: More sophisticated control systems

### Operating Cost Analysis

#### Compressed Air Consumption

Energy costs differ significantly between designs:

**Single-Acting Air Usage:**

- **Extension only**: Air consumed during extension stroke
- **Holding position**: Continuous air supply required
- **Return stroke**: No air consumption (spring powered)
- **Typical consumption**: 0.5-1.5 SCFM per cycle

**Double-Acting Air Usage:**

- **Both directions**: Air consumed for extension and retraction
- **Position holding**: Pilot air only with proper valve design
- **Higher flow rates**: Faster cycling requires more air
- **Typical consumption**: 1.0-3.0 SCFM per cycle

#### Energy Cost Calculation Example

For a typical application running 16 hours/day, 250 days/year:

| Parameter | Single-Acting | Double-Acting | Annual Difference |
| Air consumption | 1.0 SCFM | 2.0 SCFM | 1.0 SCFM more |
| Operating hours | 4000 hrs/year | 4000 hrs/year | Same |
| Air cost | $0.25/1000 SCF | $0.25/1000 SCF | Same rate |
| Annual energy cost | $60 | $120 | $60 more |

### Productivity and Performance Benefits

#### Cycle Time Improvements

Double-acting cylinders enable faster operation:

**Cycle Time Comparison:**

- **Single-acting**: Limited by spring return speed (typically 2-5 seconds)
- **Double-acting**: Optimized speeds in both directions (0.5-2 seconds)
- **Productivity gain**: 150-400% improvement in cycle rate
- **Revenue impact**: Significant production increases possible

#### Quality and Precision Benefits

Positioning accuracy affects product quality:

| Quality Factor | Single-Acting Impact | Double-Acting Impact | Business Value |
| Positioning accuracy | ±2-5mm typical | ±0.1-0.5mm typical | Reduced rejects |
| Repeatability | Variable with load | Consistent performance | Better quality |
| Force control | Limited capability | Precise force control | Process optimization |
| Speed consistency | Load dependent | Load independent | Predictable output |

### Maintenance and Reliability Costs

#### Maintenance Requirements

Maintenance costs vary between designs:

**Single-Acting Maintenance:**

- **Spring replacement**: Springs fatigue over time
- **Seal replacement**: Fewer seals but critical
- **Cleaning**: Simple design easier to maintain
- **Typical interval**: 500,000-2,000,000 cycles

**Double-Acting Maintenance:**

- **Seal replacement**: More seals but predictable wear
- **System cleaning**: More complex but better diagnostics
- **Preventive maintenance**: Scheduled based on cycle count
- **Typical interval**: 1,000,000-5,000,000 cycles

#### Failure Mode Analysis

Different failure patterns affect costs:

| Failure Type | Single-Acting | Double-Acting | Impact |
| Seal failure | Immediate loss of function | Gradual performance loss | DA: Better warning |
| Spring failure | Complete loss of return | N/A | SA: Critical failure |
| Contamination | Simple cleaning | Complex cleaning | SA: Easier service |
| Wear patterns | Uneven spring wear | Predictable seal wear | DA: Planned maintenance |

### Return on Investment Analysis

#### ROI Calculation Methodology

Consider these factors for ROI analysis:

**Cost Factors:**

- Initial equipment investment
- Installation and setup costs
- Operating energy costs
- Maintenance and replacement costs

**Benefit Factors:**

- Increased production capacity
- Improved product quality
- Reduced labor costs
- Decreased downtime

#### Typical ROI Scenarios

**High-Volume Production Application:**

- **Additional investment**: $800 for double-acting system
- **Productivity improvement**: 200% increase in cycle rate
- **Quality improvement**: 50% reduction in rejects
- **Annual savings**: $15,000-25,000
- **ROI period**: 2-4 months

**Medium-Volume Precision Application:**

- **Additional investment**: $1,200 for double-acting system
- **Positioning improvement**: 90% better accuracy
- **Maintenance reduction**: 40% fewer service calls
- **Annual savings**: $8,000-12,000
- **ROI period**: 6-12 months

### Decision Matrix for Selection

#### Application Scoring System

Use this matrix to evaluate cylinder type selection:

| Evaluation Criteria | Weight | Single-Acting Score | Double-Acting Score |
| Initial cost sensitivity | 20% | 9/10 | 6/10 |
| Precision requirements | 25% | 3/10 | 9/10 |
| Cycle rate needs | 20% | 4/10 | 9/10 |
| Force control needs | 15% | 3/10 | 9/10 |
| Maintenance simplicity | 10% | 8/10 | 6/10 |
| Energy efficiency | 10% | 7/10 | 5/10 |

Jennifer, who manages procurement for a Colorado electronics manufacturer, shared her experience: “Initially, I chose single-acting cylinders to save $3,000 on our assembly line. Within six months, we lost $18,000 in productivity due to slow cycle times and positioning problems. After switching to Bepto’s double-acting rodless cylinders, we recovered the investment in four months and continue saving $2,500 monthly through improved efficiency.”

## Conclusion

While single-acting pneumatic cylinders offer lower initial costs and simpler operation, double-acting cylinders provide superior performance, precision, and productivity that typically justify their higher investment through improved operational efficiency and reduced total cost of ownership.

### FAQs About Single Acting vs Double Acting Pneumatic Cylinders

### **Q: When should I choose a single-acting cylinder over a double-acting cylinder?**

Choose single-acting cylinders for simple lifting applications, safety systems requiring fail-safe spring return, cost-sensitive projects with basic requirements, and applications where gravity or external forces assist the return movement, typically saving 20-40% on initial investment.

### **Q: How much more compressed air do double-acting cylinders consume?**

Double-acting cylinders typically consume 50-100% more compressed air than single-acting cylinders because they use air for both extension and retraction, but this increased consumption is often offset by faster cycle times and improved productivity in most applications.

### **Q: Can single-acting cylinders be converted to double-acting operation?**

Single-acting cylinders cannot be converted to double-acting operation because they lack the second air port and internal piston sealing required for bidirectional air supply, requiring complete cylinder replacement to achieve double-acting functionality.

### **Q: Which cylinder type is better for vertical mounting applications?**

Double-acting cylinders perform better in vertical mounting because they provide powered movement in both directions regardless of gravity effects, while single-acting cylinders may struggle with vertical extension against gravity or require spring assistance for proper operation.

### **Q: How do maintenance costs compare between single-acting and double-acting cylinders?**

Double-acting cylinders typically have 40-60% lower maintenance costs despite having more seals because they experience more balanced wear patterns and predictable maintenance intervals, while single-acting cylinders suffer from spring fatigue and uneven loading that leads to more frequent unexpected failures.

1. “6.2: Single-Acting Cylinder Operation”, `https://eng.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/Fluids_1%3A_Fluid_Power_and_Pneumatics_%28NWTC%29/06%3A_Single-Acting_Cylinders/6.02%3A_Single-Acting_Cylinder_Operation`. The source explains that spring-return single-acting cylinders use compressed air for one stroke and an internal spring for the return stroke after pressure is released. Evidence role: mechanism; Source type: research. Supports: Single-acting pneumatic cylinders use compressed air for movement in one direction only with spring or gravity return. [↩](#fnref-1_ref)
2. “4.1: Actuators – Cylinders”, `https://eng.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/Fluids_1%3A_Fluid_Power_and_Pneumatics_%28NWTC%29/04%3A_Basic_Circuits_using_Cylinders/4.01%3A_Actuators_-_Cylinders`. The source describes double-acting pneumatic cylinders as using air pressure through ports to extend and retract the piston in both directions. Evidence role: mechanism; Source type: research. Supports: double-acting cylinders have two air ports enabling powered movement in both directions. [↩](#fnref-2_ref)
3. “Fail-Safe System Design”, `https://www.iacsengineering.com/fail-safe-system-design/`. The source defines fail-safe design as moving equipment to a safe state during fault, power loss, or communication failure. Evidence role: general_support; Source type: industry. Supports: fail-safe operation on air loss. [↩](#fnref-3_ref)
4. “7: 3/2 Directional Control Valves”, `https://eng.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/Fluids_1%3A_Fluid_Power_and_Pneumatics_%28NWTC%29/07%3A_3_2_Directional_Control_Valves`. The source explains the 3/2 directional control valve and its use with single-acting cylinders, supporting the simpler control architecture described in the article. Evidence role: mechanism; Source type: research. Supports: 3-way valve instead of 4-way valve. [↩](#fnref-4_ref)